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- Title
Priority queueing systems: from probability generating functions to tail probabilities.
- Authors
Tom Maertens; Joris Walraevens; Herwig Bruneel
- Abstract
Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discrete-time queueing systems, we have to invert probability generating functions, since most important distributions in discrete-time queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabilities of two particular random variables in discrete-time priority queueing systems, by means of the dominant singularity approximation. We show that obtaining these tail probabilities can be a complex task, and that the obtained tail probabilities are not necessarily exponential (as in most "traditional" queueing systems). Further, we show the impact and significance of the various system parameters on the type of tail behavior. Finally, we compare our approximation results with simulations.
- Subjects
PROBABILITY theory; QUEUING theory; MANAGEMENT science; STOCHASTIC processes; GENERATING functions; PARAMETERS (Statistics); RESEARCH; SIMULATION methods &; models; SYSTEMS engineering
- Publication
Queueing Systems, 2007, Vol 55, Issue 1, p27
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-006-9003-8